基于动态权值的B-Spline光顺算法

在计算机辅助设计、虚拟现实、数字多媒体系统设计中,B样条曲线是一种进行几何形状设计和构建真实感图形的重要工具。曲线的光顺性对最终产品的外观质感有着直接影响。文章在前人研究的基础上,给出了一种基于能量的及动态权值光顺算法（DWEF）。DWEF在改进传统能量优化方程的基础上加入“运行时加权”的概念。应用DWEF使得系统能够智能地对不同曲线采取不同的光顺参数,以取得更好的光顺效果。     

相贯线作图的一种新方法

用解析法探讨了两轴线相交的回转面的相贯线投影的形状，分析了双曲线的一些相关特性，在此基础上给出了相贯线投影作图的新思路；利用实例说明了具体的作图过程。     

B样条曲线逼近的一种新方法

基于B样条曲线拟合出现的问题和困难,提出了一种新的B样条曲线拟合方法.该方法成功地避免了数据点参数化的问题,并使得逼近曲线具有较好的形状和接近弧长参数化的节点向量.本方法基本思想是:先用易于控制形状的低阶曲线拟合数据点,此曲线称为控制曲线,然后用高次曲线逼近该控制曲线,此高次曲线称为逼近曲线.根据本方法,设计新的拟合目标函数,通过求解二次优化系统来求解逼近曲线,并充分利用控制曲线提出一种新的接近弧长参数化的节点向量的设置方法.     

NURBS曲线形状微调

针对非均匀有理B样条(NURBS)曲线形状微调的一种新方法。插值NURBS曲线控制点构造一条B样条曲线,通过调整插值B样条曲线的控制点来调整NURBS曲线的形状。此外,用权点表示控制点,通过调整权点可以交互地修改NURBS曲线的形状。实验结果表明,该方法在解决NURBS曲线形状调整的效率上十分有效。     

G2保形的分段4次广义Ball插值曲线

文章给出了构造保形插值曲线的一种方法,即在每2个型值点之间构造一段4次广义Ball曲线,所构造的插值曲线是G2连续的而且是保形的,曲线可以作局部修改,曲线的形状可以由参数调节,最后给出了数值实例。     

基于PS-Level Set的嘴唇几何形状定位模型

针对面向唇读的水平集模型在嘴唇分割中存在边界过收敛和过早收敛的问题,文中提出了一种改进的基于先验知识的水平集模型(简称为PS-Level Set)来进行嘴唇几何形状的定位.PS-Level Set模型利用改进的差值能量函数引入嘴唇形状的先验信息.在曲线演化过程中,反复比较演化曲线和先验曲线的差距,使曲线的演化形状逐渐逼近先验模型形状,从而更精确地收敛于目标物体实际轮廓.实验表明,用PS-Level Set模型定位嘴唇几何形状的准确率比用水平集模型提高了8.38%.     

基于PS-level set嘴唇几何形状定位模型

针对面向唇读的level set模型在嘴唇分割中存在边界过收敛和过早收敛的问题,本文提出一种改进的基于先验知识的水平集模型（Prior Shape -level set,简称PS-level set）来进行嘴唇几何形状的定位。PS-level set模型利用改进的差值能量函数引入嘴唇形状的先验信息。在曲线演化过程中,反复比较曲线和先验曲线的差距,使曲线的演化形状逐渐逼近先验模型形状,更精确地收敛于目标物体实际轮廓。实验证明用PS-level set模型定位嘴唇几何形状的准确率比level set模型提高了8.38%。     

中国经济增长与环境污染关系实证研究

运用1999-2005年中国29个省市的面板数据,选取8种具体的环境污染指标,对中国的经济增长与环境污染关系进行实证检验,考察二者之间是否存在环境库兹涅茨曲线关系。实证结果表明,二者的关系是不确定的,并不是全部的环境质量指标与经济增长指标之间都存在环境库兹涅茨倒U型曲线关系,有一些指标也呈现倒N型和线性关系,曲线形状与环境指标的选取和样本数据的选择有极大的关系。     

三次保形有理插值

构造了含有4个参数的分段三次有理样条函数(分子、分母均为三次多项式),其中2个参数称为形状参数,另外2个称为保形参数;通过调整形状参数可交互式修改曲线形状,适当选取保形参数曲线是保单调的。数值例子显示由该样条函数生成的曲线十分光滑且保持了数据固有的形态,最后给出了此插值函数的误差估计。     

面向三维参数化女性人台构建的胸部特征数据测量方法

为了在计算机中实现三维参数化人台的显示与调节，并能真实地反映人体各围度曲线的变化，本文通过三维激光非接触式人体扫描仪，对300余名在校女大学生进行测量，获取了大量的人体长度和围度方向的测量数据．通过对胸部测量数据的统计分析，选择了能够反映女性胸部形状和形态的5个水平截面，提取了影响曲线围度形状的特征点．对特征点坐标与身高及反映胸部体型的参数进行了多元线性回归分析，得出构成胸部各围度曲线的特征点坐标变化规律，实现了女性参数化人台胸部曲线的真实模拟．     

切线曲面的斜等距曲面及其性质

斜等距曲面原理在机械加工中有着广泛的应用,因此,对斜等距曲面的性质进行研究具有实际意义,我们已经证明了锥面、柱面的斜等距曲面的一些性质,将证明切线曲面的斜等距曲面的一些性质,并分析了切线曲面上各点邻近处点的形状,由于在实际应用中,我们需要知道根据模型加工出的曲面能否达到要加工的曲面的形状要求,因此对曲面上各点形状的分析对实际应用具有指导作用。     

Curve interpolation based on Catmull-Clark subdivision scheme

An efficient algorithm for curve interpolation is proposed. The algorithm can produce a subdivision surface that can interpolate the predefined cubic B-spline curves by applying the Catmull-Clark scheme to a polygonal mesh containing "symmetric zonal meshes", which possesses some special properties. Many kinds of curve interpolation problems can be dealt with by this algorithm, such as interpolating single open curve or closed curve, a mesh of nonintersecting or intersecting curve. The interpolating surface is C2 everywhere excepting at a finite number of points. At the same time, sharp creases can also be modeled on the limit subdivision surface by duplicating the vertices of the tagged edges of initial mesh, i.e. the surface is only C0 along the cubic B-spline curve that is defined by the tagged edges. Because of being simple and easy to implement, this method can be used for product shape design and graphic software development.     

A new method for automatically constructing convexity-preserving interpolatory splines

Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous. The method is simple and convenient, and the resulting interpolating curves possess smooth distribution of curvature. Numerical examples illustrate the correctness and the validity of theoretical reasoning.     

G3 continuous curve modeling with rational cubic Bézier spline?

Based on the study of some intrinsic properties of the weights of rational Bézier curve, it has been found that the shape of a curve can be changed by adjusting the weights without moving its control points. An approach for improving the geometric continuity order between two adjacent curves by modifying the weights is presented. The G3 continuity conditions for two adjacent curves are first derived, which reveals that the geometric meaning of G3 continuity is torsion continuity. A constructive method is then presented to blend two rational Bézier curves with G3 continuity. Finally, the proposed method is used to construct closed G2 curves, or G3 curves by changing or inserting one control point.     

G3 continuous curve modeling with rational cubic Bézier spline

Based on the study of some intrinsic properties of the weights of rational Bézier curve, it has been found that the shape of a curve can be changed by adjusting the weights without moving its control points. An approach for improving the geometric continuity order between two adjacent curves by modifying the weights is presented. The G3 continuity conditions for two adjacent curves are first derived, which reveals that the geometric meaning of G3 continuity is torsion continuity. A constructive method is then presented to blend two rational Bézier curves with G3 continuity. Finally, the proposed method is used to construct closed G2 curves, or G3 curves by changing or inserting one control point.     

新型水驱特征曲线系列(Ⅱ)

针对目前在国内用得比较多的4种水驱特征曲线所存在的问题,提出了一种既简单又综合了甲乙两种类型关系的f _w—R*水驱特征曲线。将丙型与丁型结合提出新的水驱特征曲线,并和经典的水驱特征曲线完全等效的一种水驱特征曲线表达式,同时又能反映含水率-采出程度关系的多条曲线,对它的形状和性质作了一些研究,指出今后水驱特征曲线的研究方向是找出更简单、准确、实用的广义水驱特征曲线。通过实例计算表明,所建立的新型水驱特征曲线与实际数据拟合相关性更强,结果更可靠。     

A new method for compression-rebuilding of IR spectra

This work presents a new spectral data compression-rebuilding technique to translate the full IR spectral data into compact codes based on the analysis and comprehension encoding approach. This method has been successfully applied to a sample set of 505 IR spectra randomly picked from 100 000 spectra. The results show that the compression ratio reaches 12.7:1 under a very weak curve distortion. The choice of the number and shape of the basis functions is flexible. The IR spectra can be compressed in a fixed data size in fulfilling the distortion criteria. The data after compression have no significance in the sense of 蜶 spectra. To recover the original spectra, a specific algorithm must be applied. So the method can be used as a cryptic tool. Furthermore, the method can be applied to the compression of other complex curve by utilizing some of proper basis functions.     

不连续细长相方位分布与CMCs增韧特性

通过分析得出不同压缩条件下的增强相定向度概率分布函数，计算获得裂纹扩展过程中的架桥应力曲线及阻抗曲线，对增韧特性的方位角依赖性进行了讨论，对架桥应力与裂纹张口位移的变化关系进行了讨论，并把计算结果与试验数据进行了对比分析．本文的力学模型基本具备分析裂纹小位移段增韧行为的要素．     

NURBS曲线的半正交小波分解算法

为了对NURBS曲线进行精确的分解，提出了半正交B样条小波分解的新算法，同时给出了处理NURBS曲线的非整数阶分辨率的小波分解算法．对于NURBS曲线，无论它有多少个控制点，均可以对它进行半正交分解，而不受控制点数必须等于2‘ 3的限制，这对于NURBS曲线的多分辨率造型具有较大的应用价值．